# Pythagoras' Revenge: A Mathematical Mystery

By Arturo Sangalli | Go to book overview

Appendix 4
A Simple Visual Proof of the
Pythagorean Theorem

The area of a square of side a + b is (a + b)2 or a2 + b2 + 2ab (I).

On the other hand, if the interior of the square is divided up into a square of side c and four right-angled triangles of sides a, b as shown below, its area equals the sum of the areas of these five figures, that is c2 + 4(ab/2) or c2 + 2ab (II).

Since the expressions (I) and (II) represent the same area, we have

a2 + b2 + 2ab = c2 + 2ab, which implies

a2 + b2 = c2

-177-

### Notes for this page

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Project items
Notes
Cite this page

#### Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

#### Cited page

Bookmark this page
Pythagoras' Revenge: A Mathematical Mystery
Table of contents

Settings

Typeface
Text size
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.
Print this page

#### Print this page

Why can't I print more than one page at a time?

While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience.
Full screen
/ 183

## Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

## Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.

Are you sure you want to delete this highlight?